Percentages and ratio · Ages 13–14

Percentages (II) worksheet

Covers: Compound interest, Compounding periods, Growth and depreciation, Changes in the parts, Chains of sellers and offers, Salaries tax

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Percentages and ratio · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.At 2% a year, compounded yearly, the amount after 3 years is $37,142.28. The principal = $
Answer:
2.$2,000 at 4% a year, compounded every 3 months, for 9 months. The amount = $ (to the nearest dollar)
Answer:
3.A new car worth $150,000 loses 25% of its value in its first year and 8% a year after that. To the nearest dollar, what is it worth after 4 years?
Answer:
4.The price rises 25% and the number sold rises 20%: the takings rise %
Answer:
5.A club has 900 men and 300 women. This year the men grow by 20% and the women fall by 5%: the membership grows by %
Answer:
6.An item costs $250 to make. The maker sells to a wholesaler at a 20% profit, for $; the wholesaler to a shop at 20%, for $; the shop sells at 25%, for $.
Fill in each blank
Answer:
7.Net chargeable income is taxed at 2% on the first $50,000, 6% on the next $50,000, 10% on the next $50,000, 14% on the next $50,000 and 17% on the rest. On a net chargeable income of $109,000: the first $50,000 pays $, the next $50,000 pays $, the remaining $9,000 pays $, $ in all.
Fill in each blank
Answer:

8.On $2,000 at 5% a year, compounded yearly, the interest for 4 years is about $400.
True or false?
Answer:
9.At 6% a year compounded every 3 months, each period's rate is 1.5%.
True or false?
Answer:
10.A website has 1000 members, and the number grows 10% a year. At the end of which year does it first pass 2000?
- A. The end of year 9
- B. The end of year 10
- C. The end of year 7
- D. The end of year 8
Choose the right answer
Answer:
11.An item sells in a shop for $192. The shop made 60% on it and the wholesaler 50%. What did the maker sell it to the wholesaler for?
- A. $38.4
- B. $80
- C. $−19.2
- D. $120
Choose the right answer
Answer:
12.Net chargeable income is taxed at 2% on the first $50,000, 6% on the next $50,000, 10% on the next $50,000, 14% on the next $50,000 and 17% on the rest. On a net chargeable income of $218,000, the salaries tax is $19,060.
True or false?
Answer:

13.A deposit earns 10% a year, compounded yearly, and grows to $39,530.7 after 4 years. What was put in?
Working:
Answer:
14.Tsz-hin has $10,000 to save for 4 years. Bank A pays 5% a year compounded yearly; Bank B pays 4.9% a year compounded every 6 months. Which ends with more?
- A. It depends on the years
- B. Bank B
- C. Bank A
- D. The same
Choose the right answer
Working:
Answer:
15.Chi-keung's dad bought a car for $120,000, and it loses 20% of its value a year. To the nearest dollar, what is it worth after 4 years?
Working:
Answer:
16.A photo is enlarged so that its length and width are both 30% bigger. By what percentage does its area grow?
Working:
Answer:
17.A supermarket's drinks are "buy 5, get 1 free", marked $9.5 a bottle. Tsz-hin takes 12 bottles. How much is paid?
Working:
Answer:
18.Net chargeable income is taxed at 2% on the first $50,000, 6% on the next $50,000, 10% on the next $50,000, 14% on the next $50,000 and 17% on the rest. There is also a standard rate of 15% on the income less deductions (no allowances), and the lower of the two is charged. Someone has $2,810,000 of income, $12,000 of deductible contributions and a $264,000 allowance. What salaries tax is charged?
Working:
Answer:

Show the answers and working

Percentages (II) worksheet: Answers and working

1. 35,000
Principal × 1.02³ = 37142.28, so the principal = 37142.28 ÷ 1.02³ = 35000. Not 37142.28 × (1 − 2%)³.
2. 2,061
Each period earns 4% ÷ 4 = 1%, and 9 months make 9 ÷ 3 = 3 periods: 2000 × (1 + 1%)³, about 2061.
3. 87,602 dollars
The first year leaves 1 − 25%, each of the next 3 years 1 − 8%: 150000 × (1 − 25%) × (1 − 8%)³, about 87602.
4. 50
Takings = price × sales: (1 + 25%) × (1 + 20%) = 1 + 50%. The factors multiply, a little more than 25% + 20%.
5. 13.75
900 × 20% = 180 more men and 300 × 5% = 15 fewer women: 165 more in all, and 165 ÷ 1200 × 100% = 13.75%. The two rates don't simply subtract.
6. 300, 360, 450
Each seller's cost is the last one's price: 250 × 1.2 = 300, 300 × 1.2 = 360, 360 × 1.25 = 450.
7. 1,000, 3,000, 900, 4,900
50000 × 2% = 1000, 50000 × 6% = 3000, 9000 × 10% = 900, so 1000 + 3000 + 900 = 4900.

8. False
Compound interest = 2000 × 1.05⁴ − 2000, about 431. $400 is simple interest, each year on the principal alone.
9. True
A year has 12 ÷ 3 = 4 periods, each at 6% ÷ 4 = 1.5%. 6% is the rate for the whole year.
10. D. The end of year 8
Multiply by 1.1 year by year until it passes 2000: 1000 × 1.1⁷ hasn't, 1000 × 1.1⁸ has.
11. B. $80
Divide back, seller by seller: 192 ÷ (1 + 60%) = 120, 120 ÷ (1 + 50%) = 80.
12. True
Band by band it is 19060. 218000 × 17% = 37060 charges every band at the top rate: too much.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 27,000 dollars
Principal × 1.1⁴ = 39530.7, so the principal = 39530.7 ÷ 1.1⁴ = 27000.
14. C. Bank A
Compare the real yearly rates: Bank A 5%; Bank B (1 + 4.9% ÷ 2)² − 1 = 4.960025%.
15. 49,152 dollars
Each year leaves 0.8 of it: 120000 × 0.8⁴, about 49152.
16. 69%
The area's factor is 1.3 × 1.3 = 1 + 69%, a 69% rise, not 2 × 30% = 60%.
17. 95 dollars
Every 6 bottles cost 5: 12 bottles are 2 lots, so 2 × 5 × 9.5 = 95.
18. 412,780 dollars
Progressive: (2810000 − 12000 − 264000) band by band, 412780; standard: (2810000 − 12000) × 15% = 419700; the lower, 412780.

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